╨╧рб▒с>■  ■                                                                                                                                                                                                                                                                                                                                                                                                                                                   rom a sold seat; P = 100; ! Penalty for a turned down customer; Q = .04; ! Probability customer is a no-show; ! No. of seats available; N = @SIZE( SEAT); ! Expected profit with no overbooking; EPROFIT0 = V * @SUM( SEAT(I): (1 - @PBN(1- Q, N, I - 1))); ! Expected profit if we overbook by 1 is: EPROFIT0 + Prob(he shows) * ( V - (V + P) * Prob(we have no room)); EPROFIT( 1) = EPROFIT0 + ( 1 - Q) * ( V - ( V + P) * @PBN( Q, N, 0)); ! In general; @FOR( EXTRA( I)| I #GT# 1: EPROFIT( I) = EPROFIT( I - 1) + (1 - Q) * ( V - ( V + P) * @PBN( Q, N + I - 1, I - 1)); ); END MODEL: ! A strategy for airlines to minimize the loss from no-shows is to overbook flights. Too little overbooking results in lost revenue. Too much overbooking results in excessive penalties. This model computes expected profits for various levels of overbooking.; SETS: SEAT/1..16/; ! seats available ; EXTRA/1..6/: EPROFIT; ! expected profits from overbooking 1-6 seats; ENDSETS ! Available data; V = 225; ! Revenue f■   ¤   ■   ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Root Entry        аCONTENTS            а                         ■                                                                                                                                                                                                                                                                                                                                                                                                                                                       Root Entry        *0_Ъю╧╗Є└Ё^ ▐дкe■─ @Contents                                                            ■   ¤   ■   ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 ■                                                                                                                                                                                                                                                                                                                                                                                                                \cf3 ! In general;\cf2 \par \cf1 @FOR\cf2 ( EXTRA( I)| I #GT# 1: \par EPROFIT( I) = EPROFIT( I - 1) + \par (1 - Q) * ( V - ( V + P) * \par \cf1 @PBN\cf2 ( Q, N + I - 1, I - 1)); \par ); \par \par \cf1 END\cf2 \par \par } ьЛ{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Courier New;}} {\colortbl ;\red0\green0\blue255;\red0\green0\blue0;\red0\green175\blue0;} \viewkind4\uc1\pard\cf1\f0\fs20 MODEL\cf2 : \par \cf3 ! A strategy for airlines to minimize the loss from \par no-shows is to overbook flights. Too little \par overbooking results in lost revenue. Too much \par overbooking results in excessive penalties. This \par model computes expected profits for various levels \par of overbooking.;\cf2 \par \par \cf1 SETS\cf2 : \par SEAT/1..16/; \cf3 ! seats available ;\cf2 \par EXTRA/1..6/: EPROFIT; \cf3 ! expected profits from \par overbooking 1-6 seats;\cf2 \par \cf1 ENDSETS\cf2 \par \par \cf3 ! Available data;\cf2 \par V = 225; \cf3 ! Revenue from a sold seat;\cf2 \par P = 100; \cf3 ! Penalty for a turned down customer;\cf2 \par Q = .04; \cf3 ! Probability customer is a no-show;\cf2 \par \par \cf3 ! No. of seats available;\cf2 \par N = \cf1 @SIZE\cf2 ( SEAT); \par \par \cf3 ! Expected profit with no overbooking;\cf2 \par EPROFIT0 = V * \cf1 @SUM\cf2 ( SEAT(I): \par (1 - \cf1 @PBN\cf2 (1- Q, N, I - 1))); \par \par \cf3 ! Expected profit if we overbook by 1 is: \par EPROFIT0 + Prob(he shows) * ( V - (V + P) * \par Prob(we have no room));\cf2 \par EPROFIT( 1) = EPROFIT0 + \par ( 1 - Q) * ( V - ( V + P) * \cf1 @PBN\cf2 ( Q, N, 0)); \par \par